Question

which of the following is the equation of a line perpendicular to the line -3/2x + 4, passing through the points (3,9)

Answer 1

We know it is perpendicular to a line of gradient -3/2, so what's the gradient of the new line?

Answer 2

Well in my notes it says the the slope of 2 perpendicular lines are negatice reciprocals that's really what I'm confused about , I'm not really sure what gradient means

Answer 3

*negative

Answer 4

Exactly, it's a negative reciprocal. Do you know what a reciprocal is?

Answer 5

Gradient is just how steep the line is

Answer 6

Ohh okay and yeah doesn't reciprocal just mean equal ?

Answer 7

Nope, it means you turn the fraction upside down. As a few examples, what are the reciprocals of these:

1. 3/2
2. 1/2
3. 6/5
4. 8

Answer 8

Ohh okay so in this problem do I flip the -3/2x to -2/3 ?

Answer 9

That gets the reciprocal, but what does the definition of perpendicular say?

Answer 10

I'm sure I sound really stupid but I'm not actually sure

Answer 11

It just says that two lines with slopes m1 ad m2 are perpendicular if and only if their slopes are negative reciprocals

Answer 12

Don't worry about how you sound, you're here to learn and there's nothing stupid about that :)

Answer 13

Yes, the negative reciprocal

Answer 14

So -3/2 goes to?

Answer 15

-2/3 ? and thank you

Answer 16

m=-3/2, what is -1/m?

Answer 17

Are you asking what the reciprocal of -1/m is ?

Answer 18

Nope, sorry I should've been more clear. The gradient is often referred to as m and in this case m=-3/2. A line perpendicular to a line of gradient m, has gradient -1/m (the negative reciprocal). So what I'm asking you to do is:
\[-\frac{1}{-\frac{3}{2}} \]

Answer 19

Sorry I am just so confused also I left out a few things so I'll retype the question
Which of the following is the equation of a line perpendicular to the line y= -3/2x + 4, passing through the points (3,9)
A. -2x - 3y = -21
B. -2x +3y = 21
C. 2x + 3y = 21
D. 2x-3y = 21

Answer 20

The negatives cancel, and 1/(3/2)=2/3 so that's the gradient of our new line. The equation of a straight line is given as (y-y1)=m(x-x1) where m is the gradient and (x1, y1) is a point on this line. We have m and a point (3,9), so we get:
y-9=(2/3)(x-3)
3(y-9)=2(x-3)
3y-27=2x-6
-2x+3y=21

So B is the answer :)

Answer 21

I'm going to bed but if you have any questions I'll answer in the morning.

Answer 22

Thank you so much !